抄録
Discussed are axial variations of five variables ‹p·p›t, AI≡‹p·A‹u›r›t, ‹p·A‹ξ›r›t, ‹‹u›r·‹u›r›t and ‹‹ξ›r·‹ξ›r›t required for calculating the heat flow AQ and the work source AW per unit length. Discussions are based on linearized forms of the continuity equation and the Euler one. The continuity equation leads to the first relationship ∇_??_(AI)=AW where A is cross-sectional area of the flow channel. The Euler equation leads to the second relationship ∇‹p·p›t={(2ωρm)/(|1-χν|2)}·[{(1-χν′)ω‹p·A‹ξ›r›t+χν″AI}/A] and the third relationship ∇_??_ψ={(ωρm)/(|1-χν|2)}·[{χν″ω‹p·A‹ξ›r›t-(1-χν′)AI}/A‹p·p›t] where ψ is phase of pressure oscillation. A couple of the continuity equation and the Euler one leads to the fourth relationship ∇_??_‹p·A‹ξ›r›t=(β∇_??_Tm)FS[χα′‹p·A‹ξ›r›t+(χα″/ω)AI]-[KS+(KT-KS)FSχα′]A‹p·p›t+{(1-χν′)/(|1-χν|2)}Aρm‹‹u›r·‹u›r›t. These equations are supplemented by the following two relationships ‹‹u›r·‹u›r›t=ω2‹‹ξ›r·‹ξ›r›t. ‹‹ξ›r·‹ξ›r›t={(‹p·A‹ξ›r›t)2}/(A2‹p·p›t)+{(AI)2}/{(Aω)2‹p·p›t}. The first, the second and the forth relationships are, therefore, three differential equations between three independent variables ‹p·p›t, ‹p·A‹ξ›r›t and AI. A wave equation is derived also from the continuity equation and the Euler one. It is used to show that the stability limit is the same as that derived by N. Rott in the case that the temperature distribution is described by a step function.
